revenue maximisation

Differing Objectives and Policies of Firms (Cambridge AS & A‑Level Economics – Topic 7.8)

1. Full List of Firm Objectives (7.8.1‑7.8.5)

Cambridge expects candidates to know the main objectives a firm may pursue, a concise definition and the decision rule that the firm would use when choosing output (and price where relevant).

Objective	Definition (one‑sentence)	Decision rule (output/price)
Profit maximisation	Maximise the difference between total revenue (TR) and total cost (TC).	Produce where MR = MC and P ≥ AVC (otherwise shut‑down). In perfect competition this is also the point where P = MC.
Revenue maximisation	Maximise total revenue irrespective of the cost incurred.	Produce where MR = 0 **and** P ≥ AVC; if P < AVC the firm shuts down.
Sales (output) maximisation	Maximise the quantity sold, usually to increase market share.	Produce where MR = 0 while keeping MC ≤ MR and P ≥ AVC. The firm will not produce if price falls below AVC.
Survival (break‑even) objective	Cover all costs in the short run so the firm can stay in the market.	Produce as long as P ≥ AVC; shut down when P < AVC.
Satisficing	Achieve an “acceptable” level of profit rather than the maximum possible.	Choose any output where profit ≥ target profit; usually where MR ≈ MC but not necessarily exactly equal.
Price discrimination	Charge different prices to different consumer groups for the same product.	Set a separate marginal‑revenue curve for each market segment and equate each to marginal cost (e.g. MR₁ = MC, MR₂ = MC).
Limit pricing (entry‑deterrence pricing)	Set a low price to make entry unprofitable for potential rivals.	Choose a price that just covers the incumbent’s costs while giving the entrant a negative expected profit.
Predatory pricing	Temporarily price below cost to force competitors out of the market.	Price ≤ AVC (or even ≤ ATC) for a short period, then raise price once rivals have exited.
Price leadership	One dominant firm sets the market price and other firms follow.	Leader chooses price where its own MR = MC; followers accept that price.
Concentration‑ratio objective (market power)	Increase the firm’s share of total industry output.	Expand output until the firm’s share of total Q reaches the desired concentration level.

2. Quick Audit of the Notes Against the Cambridge 9708 Syllabus (Topic 7.8)

Syllabus requirement (7.8)	Current coverage	Gap / issue	Actionable suggestion
7.8.1 – Profit‑maximisation	Only a brief definition and MR = MC rule.	Missing discussion of MC, AVC, ATC and the shutdown rule.	Add a concise paragraph explaining MR = MC, the condition P ≥ AVC for continued production, and why this rule applies in both perfect competition and monopoly.
7.8.2 – Revenue‑maximisation	Well‑developed, but the decision rule omits the P ≥ AVC condition.	Students may forget the shutdown rule.	Insert a one‑line note after “MR = 0” stating that the firm will only produce if price covers variable cost; otherwise it shuts down.
7.8.3 – Sales (output) maximisation	Definition and rule given, but the shutdown condition is not mentioned.	Potential confusion with revenue maximisation.	Clarify that the firm also requires P ≥ AVC and that MC must not exceed MR.
7.8.4 – Survival (break‑even) objective	Accurately described.	None.	Retain as is.
7.8.5 – Satisficing & other objectives	All listed with appropriate rules.	None.	Retain as is.

3. Revenue Maximisation in Detail

3.1 Definition and Core Formulae

• Total Revenue (TR): \(TR = P \times Q\)
• Marginal Revenue (MR): \(MR = \dfrac{dTR}{dQ}\) – the extra revenue from selling one more unit.
• Revenue‑maximising output (\(Q_R\)): The quantity at which MR = 0, i.e. the peak of the TR curve, provided that P ≥ AVC so the firm does not shut down.

3.2 Linking MR to a Linear Demand Curve

Assume a straight‑line downward‑sloping demand curve:

\[ P = a - bQ \qquad (a,b>0) \]

Substituting into the TR equation:

\[ TR = P Q = (a - bQ)Q = aQ - bQ^{2} \]

Differentiate with respect to \(Q\):

\[ MR = \frac{dTR}{dQ}= a - 2bQ \]

Key observations:

• The MR curve shares the same vertical intercept as the demand curve (a) but has twice the slope, so it lies **below** demand for any positive \(Q\).
• Setting \(MR = 0\) gives \(\displaystyle Q_R = \frac{a}{2b}\) – exactly the midpoint of the linear demand curve.
• At \(Q_R\) total revenue is at its maximum; any further increase in output reduces TR.

3.3 Elasticity and the Revenue‑maximising Decision

Recall the relationship between MR, price and price elasticity of demand (\(\varepsilon\)):

\[ MR = P\Bigl(1 + \frac{1}{\varepsilon}\Bigr) \]

• Elastic demand (\(|\varepsilon| > 1\)): \(\frac{1}{\varepsilon}\) is negative but greater than –1, so \(MR > 0\). Expanding output raises TR.
• Unit‑elastic demand (\(|\varepsilon| = 1\)): \(MR = 0\). This is the revenue‑maximising point.
• Inelastic demand (\(|\varepsilon| < 1\)): \(\frac{1}{\varepsilon}\) is less than –1, making \(MR < 0\). Further output reduces TR.

3.4 Short‑Run Implications for a Revenue‑maximising Firm

1. If the revenue‑maximising output yields TR ≥ VC, the firm will keep producing even when TR < TC (i.e. it makes a loss). Shutting down would give zero revenue, which is worse.
2. When P > AVC but P < ATC, the firm operates at a loss – a typical short‑run situation compatible with revenue maximisation.
3. Because costs are ignored in the objective, the firm may produce beyond the profit‑maximising output, leading to a higher quantity and a lower market price than a profit‑maximising rival.

3.5 Long‑Run Implications

• Persistent losses are unsustainable. The firm must either reduce its cost structure (e.g., adopt cheaper technology, achieve economies of scale) or switch to a profit‑maximising objective when market conditions change.
• Regulated monopolies may be forced by a price‑cap regulator to operate where P ≥ AVC and where total revenue is sufficient to cover long‑run average costs.

4. Comparison of the Three Main Objectives

Aspect	Revenue maximisation	Profit maximisation	Sales (output) maximisation
Primary goal	Highest possible TR	Highest possible TR – TC	Largest possible Q (market share)
Decision rule	Produce where MR = 0 and P ≥ AVC	Produce where MR = MC and P ≥ AVC	Produce where MR = 0 while keeping MC ≤ MR and P ≥ AVC
Cost consideration	Ignored for the objective; costs matter only for the shutdown condition.	Central – both MR and MC are compared.	Secondary – the firm will continue as long as MC does not exceed MR and price covers variable cost.
Typical environment	Monopolies or regulated utilities facing price caps; start‑ups chasing market share.	Most competitive firms in market economies.	New entrants, fast‑growing sectors, firms with excess capacity.

5. Evaluation – Advantages, Disadvantages and Real‑World Relevance (AO3)

5.1 Advantages of Revenue Maximisation

• Rapid market‑share growth: By focusing on sales volume, a firm can become dominant, creating barriers to entry.
• Fit for regulated industries: Utilities with statutory service obligations often need to maximise revenue within a price‑cap to fund capital investment.
• Simplicity of decision‑making: The rule “produce where MR = 0 (provided P ≥ AVC)” is easy to apply even when cost data are uncertain.

5.2 Disadvantages / Limitations

• Ignores costs: Operating at a loss is not viable in the long run; the firm may exhaust financial resources.
• Risk of over‑production: Output can exceed the efficient scale, wasting resources and potentially harming the environment.
• Consumer‑welfare concerns: Although low prices can benefit consumers initially, a later price increase after market power is achieved may reduce welfare.
• Regulatory risk: Many jurisdictions view pure revenue‑maximising behaviour in monopolies as abusive and may impose price caps or performance‑based penalties.

5.3 When Do Real‑World Firms Adopt This Objective?

• Regulated monopolies: Electricity, water and telecommunications providers often have price‑cap regulation; they aim to maximise revenue within the cap to recover costs and fund infrastructure.
• Start‑ups seeking market share: Early‑stage tech firms (e.g., social‑media platforms) may offer free or heavily subsidised services to maximise users before monetising.
• State‑owned enterprises: Some government‑run firms are instructed to maximise revenue to meet fiscal targets rather than profit.

5.4 Policy Implications

Because revenue‑maximising behaviour can lead to excessive extraction of consumer surplus or inefficient resource use, governments and regulators may intervene using:

• Price caps or rate‑of‑return regulation: Limit the maximum price a monopoly can charge, thereby restricting the revenue‑maximising output.
• Performance‑based regulation: Tie allowable revenue to service quality, investment levels, or environmental standards.
• Competition policy: Encourage entry (e.g., by licensing new providers) to reduce the incentive for a dominant firm to pursue pure revenue maximisation.

6. Suggested Diagram (single composite diagram)

Draw a diagram that includes:

• A downward‑sloping demand curve (labelled D).
• The marginal‑revenue curve (labelled MR) below D, intersecting the horizontal axis at the midpoint of D.
• The total‑revenue curve (parabolic, labelled TR) that rises, peaks where MR = 0, then falls.
• Mark the revenue‑maximising quantity Q_R on the horizontal axis and the corresponding price P_R on the demand curve.
• Optionally, add the marginal‑cost curve (MC) to illustrate the difference between revenue‑maximising and profit‑maximising outputs.

7. Key Takeaways

• Revenue maximisation is a legitimate firm objective; the decision rule is MR = 0 **and** the firm must still satisfy the shutdown condition P ≥ AVC.
• With a linear demand curve, MR lies below demand and reaches zero at the demand midpoint – the point where total revenue is highest.
• Elasticity determines the direction of revenue change: firms expand output until demand becomes unit‑elastic.
• In the short run the firm may accept losses as long as variable costs are covered; in the long run it must either cut costs or shift to profit maximisation.
• Real‑world examples include regulated utilities, start‑ups chasing market share, and some state‑owned enterprises.
• Policy tools such as price caps, performance‑based regulation and competition promotion are used to curb the potentially wasteful aspects of revenue‑maximising behaviour.